A farmer has 100 acres of available land that he wishes to plant with a mixture of potatoes, corn, and cabbage. It costs him $400 to produce an acre of potatoes, $160 to produce an acre of corn, and $280 to produce an acre of cabbage. He has a maximum of $20,000 to spend. He makes a profit of $120 per acre of potatoes, $40 per acre of corn, and $60 per acre of cabbage. How many acres of each crop should he plant to maximize his profit?

a. Create a chart to organize this information.
b. Write the objective function
c. Write all the constraints to the problem.

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hdhdhdb14mdjdh hdhdhdb14mdjdh · Answer 1 · 2021-05-14T19:03:59+02:00

B write the objective function it works best

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Palky Palky · Answer 2 · 2022-01-02T15:58:52+01:00

Objective (Profit) Function : 120 Po + 40 Co + 60 Ca

Constraint Functions : Po + Co + Ca = 100 (Land Constraint) ; Budget Constraint : 400 Po + 160 Co + 280 Ca = 20000

LET : Acres of land for Potato, Corn, Cabbage = Po, Co, Ca respectively.

Objective Function is the function to be minimised or maximised. Here, 'PROFIT' is to be maximised.

So, profit function is the objective function. Profit per acre potatoes, corn, cabbage = 120, 40 , 60 respectively.

Constraint functions denote the other conditions to be maintained, while maximising & minimising objective profit function.

Here, Land constraint & budget constraints need to be satisfied. Total acres of land for potato, corn, cabbage = 100.
Cost per acre potatoes, corn, cabbage = 400, 160, 280 respectively & total budget is 20000.

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